The square root of 8 divided by the square root of 3 =? Many won’t know the ANSWER!

How to divide square roots.
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[@brucecorbettn9bh398]

I’m 73 years old trying to refresh relearn this stuff. I remember my calculus teacher saying throw away your notebook, but I did. I see some of this stuff and say to myself, at one time I knew this and it was easy. But the fact is, if you no longer use the math you will lose it. So, don’t ever stop.

[@michellepopkov940]

As Monty Python would say: GET ON WITH IT!

[@iangraham871]

I got an A in maths at High School (UK A-level, just prior to University), but i don't think i ever knew that the product of the square roots of two numbers is equal to the square root of the product of those two numbers. It was 40 years ago, but thanks for this.

[@twentyrothmans7308]

Similar, but first year Maths at Uni, but I suspect that it just disappears through inactivity. Half the fun is reading other peoples' solutions, and their reasoning.

[@KenFullman]

If you did A level maths you definitely did know that rule. If you have many values to multiply together, it doesn't matter which order you multiply them in, the result will be the same. So call your first number (AxA), call your second number (BxB) So The product of those two numbers could be (AxA)(BxB) But if you take the product of their square roots, you'd get (AxB) Which is the square root of (AxB)(AxB) which is (AxB) squared But like I say, it doesn't matter what order you do the multiplication so (AxA)(BxB) =(AxB)(AxB) = (AxB) squared So I'm pretty sure, at one time, you must have known this.

[@user-sr2of3gu4s]

Just in my head this reduced to Sqrt (8 /3) and then to 2 * Sqrt(2/3) Which I think is the simplest process and simplest answer. By definition 2/3 is a rational number and taking SQRT of it is valid

[@rogergriffiths3345]

Yes, it’s as simple as that 👍. A waste of just over 17 min of anyone’s time

[@baseline33]

I’m pushing 90. My working life was spent in the telecommunications business. The only time I needed to work out the square root of anything was to pass the maths exams as part of my technical studies.

[@faiththrower7951]

😂😂😂😂😂

[@johnbell1184]

I always wonder what is the practical use of a specific math problem, Eg: where would we use this radical square root problem ?

[@panlomito]

I turned SQR(8) into 2SQR(2). Then multiplied by SQR(3) is 2 x SQR(2x3) = 2SQR(6)... and divided by 3 gives 2SQR(6)/3 OR (2/3)SQR(6)

[@Steve-pu4zx]

1.63299.....

[@clipperledgard524]

After all this, do you know the answer? Or you just know another way to represent the same expression?

[@russelllomando8460]

good one, thanks

[@devonwilson5776]

Greetings. The answer is 2/3 times the square root of 6. The square root of 6 divided by the square root of 3 is the square root of 8 times the square root of 3 all divided by the square root of 3 times the square root of 3. That is (8^1/2×3^1/2)÷ 3^1/2×3^1/2= 24^1/2÷ (3^(1/2+1/2))=2(6^1/2)÷3^1= 2/3(6^1/2)=1.6, rounded. I guess that one would go through all this work to show an understanding of working with radicals. Why else, when you can simply divide 8^1/2 by 3^1/2 to get 1.6?

[@kendavis8046]

A spreadsheet yields a very reasonable approximation at each stage of the process.

[@jeffreyschmiedeck4254]

This guy just rambles on . The guy on Science and Math is a better teacher!

[@saeedzafar7041]

Overexplained. This is a short video on KZbin, not a 45 min class.

[@harrymatabal8448]

I totally agree

[@TravisMcGee151]

@@harrymatabal8448Maybe you guys don’t realize that the longer the viewing time the more they get paid. Those who put videos out purposely drag them out for the $.

[@mpicard]

Depends on who you are. Sounds like you guys dont need any explqnation. This longer version will truly help a lot of people struggling to truly understand the fundamentals.

[@JuneT48]

Totally agree. All videos have very interesting content but presented laboriously slowly. I am constantly scrolling forward to get to the point.

[@danieldennis9831]

2√6/3

[@aryusure1943]

Just to be clear: radical 100 divided by radical 4 = 5. right? In other words, it's only because we can't divide by an irrational number that we have to go through all that gymnastic. But we would still have to fix this problem if it was for example: radical 8 divided by radical 4. And if I got that method right I would then come up with this answer: 2 times radical 2 / 2. So, at the end of the day if the equation contains radicals that equal irrational numbers we have to use factoring to find the solution.

[@drawfark]

Wonderful!

[@thomasmaughan4798]

Interesting. Start by factoring the numerator sqrt(2)*sqrt(4) over sqrt(3). Thats 2 * sqrt(2) over sqrt(3). Multiply top and bottom by sqrt(3) so you get 2 * sqrt(6) over 3. Some of these steps are duplicated in a similar problem.

[@danielmadden9691]

Thanks

[@apopisso6302]

The exam supervisor,” times up” .But I haven t finished the first question yet!

[@davidg4288]

OK, TLDR is rationalize the denominator and simplify. Thanks for reminding me though!

[@josephcorvino1363]

I find the little math problems very interesting. However, you talk waaaaaaayyyyyyyyyy too much. Every time I try to watch one of your videos your constant repeating of every detail begins to drive me crazy by the 2 minute mark.

[@terry_willis]

John needs to label each problem with a difficulty level (saying "Many will get this wrong" does not help us). Joseph, in your case, you are learning and getting better, so the easier problems get boring to you. So with a difficulty level label, you could skip the easy peasy ones and do the harder ones.

[@utha2665]

The videos are aimed at someone that has no experience with this type problem. You can always skip parts of the video you don't like, like I do.

[@C-man553]

Exactly.

[@user-pt5pp3le2f]

Would be much simpler to say the way to get rid of the irrational denominator is to multiply the numerator and denominator by the denominator. Then, using the rules of exponents, the denominator becomes 3 and the numerator becomes the sq rt of the products, ie. sq rt of numerator and denominator, which is 24. Then one can look for factors of 24, one of which is a perfect square (4x6), 4 being a perfect square. etc.

[@stuartyoung5728]

If a transcendental number such as pi or e in the denominator, then it's stuck there.

[@alext8828]

Not really. You can always multiply by the dirigible of the recipient.

[@tomtke7351]

(+/-2×sqrt(6))/3 like proper manners at the dinner table you're not supposed to have a radical (sqrt sign) in the denominator of a fraction. So multiply numerator and denominator by [sqrt(3)]. The backbone of algebra is do the same to both parts: (-1-) equation: same on left and right side. (-2-) fraction: same on numerator and denominator.

[@stevereade4858]

Square both sides, divide, take square root. (8exp0.5/3exp0.5)exp2=xexp2. x=(8/3)exp0.5 Cuts several (confusing) steps!

[@albertmoore4445]

1.633 or roughly .015 more than the Golden Ratio, close to the same as 5/3, (Fibonacci #5 over #4)

[@stuartyoung5728]

Two thirds the square root of six.

[@jeromesassani9537]

You should memoprize the Sqrt of 2,3, and 8. sqrt 0f 2 = 1.414. sqrt of 8 is twice the sqrt of 2 or 2.828. sqrt 0f 3 = 1.732.

[@williamdelmar3964]

As an engineer We can get the answer for all practical purposes. So, what you said, to however significant figures you need.

[@jeromesassani9537]

@@williamdelmar3964 For classroom situations. I am from pre-calculator times and wasn't a math or physics major.

[@williamdelmar3964]

Similar here, precalculator educated. Memorizing a few key results and numbers, makes it easier to check your slide rule answer.@@jeromesassani9537

[@johnwsimpson3153]

(2/3)x(sqrt(6) ) and 2x(sqrt(2/3)) are both correct answers. They are equal to each other. The instructor got the first one, and the second is the result if the instructor's ban on square roots in the denominator is ignored. There is nothing wrong with square roots in the denominator. Irrational numbers and rational numbers are both real numbers. There is nothing wrong with dividing by an irrational number. The result will not be a rational number, but it will be a real number.

[@sirechoe1236]

I worked it out on pen and paper the way I did it 55 years ago. I came up with 1.633. You know 3x3=9, too much. 2x2=4, too much. Keep breaking both numbers down from there. 2.8x2.8=7.84, too small. 1.7x1.7=2.89, too small. next is 2 place decimals followed by 3 place decimals.

[@innocentodenigbo7284]

That's interesting.

[@shaggyrandy1264]

You are good

[@mariaolaciregui2128]

👍👍

[@tpobrienjr]

2x1.4142/1.7321 no radicals.

[@harrymatabal8448]

Just loves his voice

[@smokert5555]

Cool, but my calculator says 1.63. I though we were shooting for actual numbers and not another equation.

[@user-zx2qi9ru4z]

Would 2sqrt(2/3) be acceptable?

[@danluzurriaga6035]

no

[@peacemaker1122]

Well i got 1.63 and checked with my calculator and it thinks the same, how are we both wrong?

[@56edb]

I did sq rt of 8 divided by sq rt 3 and got 1.63 on my calculator. When i pressed the equal button gave me 2/3 sq rt 6.

[@dustmaker1000]

This is why I always struggled on tests…. I calculated (sq rt of 16 x sq rt of 1.5)/3….. or (4*sq rt of 1.5)/3……. This calculates to the same answer of approx 1.63 but this instructor says if the answer isn’t (2* sq rt 6)/3 then the answer is wrong even though the end calculated number is the same

[@MerryDrums]

Oops, in my haste forgot to deal with √24 which = √4 x √6 = 2 √6 therefore correct answer is 2 √6 all divided by 3

[@larrydickenson8922]

Any math problem (or physics, geometry, engineering, chemistry, etc) needs to come with a set of instructions such as decimals to 3 places, fractions in the lowest terms, no radicals in the denominator, no fractions under the radical, and on and on and on. Otherwise don’t judge the form of the solution.

[@user-ic8mt6jq1z]

more words problem , por favor

[@dnarna8994]

At the end, why not take the (+ve) and (-ve) root of 6???

[@gavindeane3670]

The √ symbol means "principal square root of" not "both square roots of".

[@albertmoore4445]

Dad, can you help me with this birdhouse I'm building, you're a math professor. Sure, Son, what is the problem? I'm supposed to make the short side the square root of 8 divided by the square root of 3 inches long, and I don't know how long that is. Oh, that's easy, it's 2 times the square root of 6 over 3! Thanks, Dad!

[@mathmandrsam]

The answer is 1.63... type sqrt(8) / sqrt (3) = and you're there.

[@glenwardgross366]

(out of the classroom many years) John why can't you take the radical sign out of the problem since you have one on top and bottom? Does dividing a radical symbol by a radical symbol just gives you one which you used to great your one with super powers? JAT Love math

[@afre3398]

The real reason is more about preforming a long division with a irrational number in the denominator is not doable. At least before the electronic calculator days. It is not wrong by any mathematical rule. But your answer will always be an approximation when calculating to get a value. NO matter if you write SQR(8)/SQR(3) or (SQR(8)*SQR(3))/3 It is more a relic from the old days with only using a slide rule. I come from a science/engineering background. And we see radicals in the denominator all the time. But in the modern days of calculators we do not care

[@jennifergrebner6994]

You have to be able to divide the top and bottom of the fraction by the same number. A radical sign is not a number. Taking the square root of a number is the opposite of raising the number to the 2nd power. What integer times itself will give you the number underneath the square root sign? It's no the same number for 8 & 3.

[@thomasmaughan4798]

@@jennifergrebner6994 Square roots of non-integers (positive real numbers) exist and are relatively easy but actually calculating one usually involves logarithms. You can raise any positive real number to any real number power, even negative exponents. In this example, you multiply the top and bottom by the same number, in this case the square root of 3, to "rationalize" the denominator and make it simply 3. The top now has an extra square root of 3 times the square root of 2, they combine to become the square root of 6.

[@PYTHAGORAS101]

This seems a bit convoluted and while the result is correct, it is not quite satisfactory to me. The result of the division of two square roots is always the square root of the division of the integers. So, the answer is simply sqrt (8/3) = sqrt (2.666...) = 1.633

[@michaelkeffer504]

(2√6)/3 is the answer.

[@mattseclecticreviews3614]

If you are going for the lowest number of factors, the “answer” is 4 / sqrt(6). As others have commented, the idea that “you can’t divide by an irrational number” seems to be a matter of preference. I know of no mathematical rule that makes any answer “invalid”. This problem has many “answers”. No matter how you express the “answer”, the answer will still have an irrational number somewhere. And all answers “resolve” to an irrational number in itself. Just like “you can’t divide by the sqrt(3) because you don’t know it’s value precisely”, try multiplying 2/3 ~= 0.6666… by the sqrt(6). You still can’t get a precise value, only an approximation. If there is a definitive mathematical rule, I’d like to know it. BTW, ChatGPT, although not perfect, does not know of any mathematical rule regarding this subject.

[@user-cg5xv4zz2b]

I went to eng school. Your numbers have to be in the form of a real number. and it is known that it is an approx - you just have to figure out the error level of observation and put that in - to give you number of digits to the right of the decimal. when you have to calculate flow through a pipe, or get the stresses on a beam - you have to use real number. Bottom line.

[@stevewthespider]

I hate irrational numbers as they are impossible to measure with tape measures or yard/meter sticks.

[@mariaolaciregui2128]

I did not place because y could not place de square roof, but I got it. Thank you

[@afre3398]

The real reason is more about preforming a long division with a irrational number in the denominator is not doable. At least before the electronic calculator days. It is not wrong by any mathematical rule. But your answer will always be an approximation when calculating to get a value. NO matter if you write SQR(8)/SQR(3) or (SQR(8)*SQR(3))/3 It is more a relic from the old days with only using a slide rule. I come from a science/engineering background. And we see radicals in the denominator all the time. But in the modern days of calculators we do not care

[@utha2665]

Not sure it was a typo, but I saw you cut and paste the same response in another thread. It's perform not preform, I'm leaning towards a typo, the rest of your sentence makes perfect sense. 😊

[@user-gj6kh2rd6q]

i like these

[@user-yl3wk1xk4w]

4.9

[@harrymatabal8448]

2√2/√3

[@mollymam7153]

2radical6 divided by 3

[@C-man553]

Mr. Roberts does irrationals.

[@matsonnerby]

To be honest, I don’t understand why one of these is a question, and the other is an answer.

[@aryusure1943]

@matsonnerby Indeed! But he never tells all the story. So we have to figure out the logic by ourselves sometimes. See my comment if you will. I try to fill the void.

[@gavindeane3670]

Exactly.

[@oyesolaayobami6238]

2/3√6

[@mrjesabi]

Get to it already

[@MerryDrums]

Answer equals √24/3

[@kk6aw]

1.63...

[@richardjohnston3031]

All of you complaining about the length of the class should get extra homework! LOL

[@johnplong3644]

Well you can’t have a radical in the denominator That is a clue

[@stevenfisher5320]

“Prahhms”?.?

[@shakirhamoodi5009]

1.63

[@ernestcook4285]

7.111

[@krisswegemer1163]

No irrational numbers in the denominator is a weird preference, not a rule. It has no mathematical significance and is not practiced with any consistency. The same people who would not put the square root of 3 in the denominator would put pi in the denominator.

[@keithschipiour4684]

I dont know never seen a square root .What kind of plant or tree has a square root ?

[@thomasmaughan4798]

"What kind of plant or tree has a square root ?" Koa wood. That's why it is so expensive.

[@brocksprogramming]

Radicals have never been my strong point as I'm quite mild.😅

[@kennethwright870]

2✔️6/3

[@gavindeane3670]

What's the reason for disallowing an irrational number in the denominator? Obviously there's no problem with that mathematically. Is it just a requirement of the syllabus that the kids you're aiming this at are taught?

[@syedmdabid7191]

Eheu!!! Id est 4√6/3vel √(8/3) responsimus.

[@patriciagreen2365]

The denominator can't contain a radical sign. Also known as a square root.

[@silverhammer7779]

Says who?

[@martinfiedler4317]

@@silverhammer7779 That rule stems from the time of the slide rule. You can easily approximate the square root - and even the cube root - in the numerator. But for the division by the denominator you have to use either natural numbers or reasonably accurate decimals. Depends on how the scales are lain out on typical slide rules. Edit: Obviously, the rule is outdated and meaningless today. You can easily divide by a root-expression with a modern calculator or computer. But Mathematicians are extremely conservative .... 😉

[@keninnewmexico8763]

Thanks for this! I've left my own sparky response to the content contributor regarding the "not allowed" irrational denominator. But I'd never known why. I really want to learn to use a slide rule, oh and buy one. I already have a few pocket protectors, so I'm good there. I have a math degree circa 1992, and have never even attempted to figure out a slide ruler. I need to change that!

[@patriciagreen2365]

Hi Ken, Thank you for replying to my comment. I really appreciate it. Although I am 69 years old, I don't know how to use a slide rule or have even seen one. When I was in college, we used calculators. I would like to learn how to use a slide rule. That sounds interesting. I hope everything is great in New Mexico.

[@gavindeane3670]

Yes it can. Mathematically, that is absolutely fine.

[@googolian]

Cos 45degrees is expressed as1/sqrt2 by the all other teachers except himtan

[@markprange2430]

Tan 30° = ?

[@markprange2430]

Diameter of a circle ≡ ?

[@leightonscycles9915]

So what's the point? After all that work where does it get you? To me you still have a number that doesn't mean anything!

[@mikechappell4156]

I thought this was just simplifying and normalizing. There is no rule against dividing by irrationals.

[@batavuskoga]

Why isn't it allowed to have a square root in de denominator ? I know perfectly how to get rid of the square root in the denominator

[@thomasmaughan4798]

Many of these problem examples are part of a much larger formula or equation. Simplifying as you go along *usually* helps in the long run. Very complex formulas can gradually build up errors if you do everything numerically (calculator, decimal approximations).

[@C-man553]

Agonizing.

[@mariaolaciregui2128]

2/3 square root of 6

[@martinfiedler4317]

Approximately 5/3...

[@christopherellis2663]

¾ thre quarters. Nobody came fourth

[@kimchee94112]

Square root of 3 is allowed everywhere.

[@G0LGS]

I don't see how the answer with a Square root is any better than the question you started with - I pretty sure if I had been asked the question at school in the 70's I would have been expected to write and answer to a few decimal places and not just as another expression.

[@bobcornwell403]

I came up with: sqrt of 8/3.

[@gavindeane3670]

Me too. I don't know where this requirement to not have an irrational in the denominator comes from.

[@thomasmaughan4798]

"sqrt of 8/3." Slightly ambiguous. Is that( square root of 8) over 3, or square root of ( 8 over 3 ) ?

[@jimyoung-gy9lx]

You take too long to get to the poiht 😩

[@Robert-jh8yo]

55?

[@Robert-jh8yo]

.7.1?

[@MartinHermans-dw3is]

This is way too long an answer to this problem.

[@davidlockwood9915]

Far too long. Drives you nuts.

[@drdentin3215]

sq rt 3 as denominator goofed me. I stopped there. Walk of shame.

[@SteveSearle]

So you still have not given an answer, you have only simplified the equation.

[@thomasmaughan4798]

"you have only simplified the equation." Congratulations. That was the task.

[@canman5060]

I learnt this in grade 6 equivalent in Hong Kong elementary school many decades ago ! Still remember !!

[@beresfordsmith1830]

That's not the answer regardless of what you had learnt in grade 6. You don't know how to do it, or else you would have done so and show your answer. Please learn how to answer a question and not play smart.

[@HelenMontgomery]

You lost me in the middle

[@larrydickenson8922]

The answer is the square root of 2.6666666 ad infinitum. Get out you calculator or log tables.

[@chrisatkins7959]

Please tell me why the average person needs to know this type of math? 90% of the population ( maybe more ) will never use this.

[@C-man553]

Good for the mind. Teaches logic and patience. Sad that we hear your question many times.

[@thomasmaughan4798]

"Please tell me why the average person needs to know this type of math?" Ten percent off a $15 item of clothing = ? You ought to be able to do this kind of simple algebra in your mind so that when you go to the checkout, you already know what to expect. Unfortunately, my adult offspring, product of a public education, cannot solve this problem nor even set it up on a calculator.

[@thomasmaughan4798]

Square roots are often used in diagonals to solve Pythagorean's Theorem. I have no idea what is an "average person" but many trades use this level of math.

[@apopisso6302]

@@thomasmaughan4798we doctors and lawyers don’t need this.

[@Peterseng24]

Start at 9:20. Way too long a video for such a simple problem. 🇦🇺

[@meshulamoren8633]

3÷6√2

[@moshes218]

עעע

[@rogergriffiths3345]

Glad this guy didn’t teach in my department. Answer is achievable by mental arithmetic for goodness sake!

[@TheMathManProfundities]

What's with all the rubbish about turning an irrational problem into a rational one? That would be alchemy and is not possible. And guess what, you failed, your answer is still irrational. Probably your worst statement was that you can't divide by √3, yes you can, even with your unnecessary rational restriction (√3/√3 is rational). All you've done here is to simplify an expression, rationality has nothing to do with it.